For the inquisitive, off the regular and without constant pestering by a guide, here's your Travel cheatsheet for The City of Lakes..
Visit the City Palace on the banks of Lake Pichola. (Only if you have a historic inclination - Can easily skip if there's a time crunch). You would be lucky to get an entry without an hour's wait here during the peak season. Also the main feature of the place is the Crystal Gallery which is a separate ticket and bit expensive if you are on budget travel and not fancy to see coloured crockery set, one for each day of the week.
Lake Pichola is a must visit (Though you would get a view of it if staying near to the ghats) would still insist going to it's banks - there's a cable car that runs nearby. Do take a ride if time permits. In between the lake are two islands - One is Lake Palace, owned by Taj Group and the other is Jagmandir (mostly used for destination weddings - There ought to be one happening in the marriage season. If lucky you might bump into one of the Bollywood celebs or luckier .. Shakira / Beyonce.. :P)
If you have your own vehicle great or else hire a cab and do visit Sajjan Garh - It's a fort on the highest mountain of Udaipur (Panaromic views of the city and stunning sunset)
Fatehsagar is another tourist attraction with a local flavour. This lake is more accessible to public and offers many water sport activities. Even though a scooter ride would entice you more would suggest a peaceful half an hour boat ride. You can carry alcohol in the boat (without say in coke bottles). Further to this lake is Badi lake. It is a good 40 min bumpy ride from Fatehsagar but worth if you are looking for some photography or better the Insta "Baahubali" place.
Now for the eating part..
The ghats alongside Pichola lake have numerous small eating joints (you might also find good stuff if you ask them) - There are ample eateries and cafes overlooking the lake (famous one that can be recollected - Jheel Cafe or Sun and Moon Cafe). For the sweet tooth monsters like me, order from The Bake Affair (closest to a German Bakery in taste too and not just because the patisserie is run by school batchmate :).. As for the Rajasthani sweets, if you are visiting in winters grab Jalebi, Imarti, Rabdi and Badam Milk from the many sweet corners of the city.
For a heavy meal try the Natraj thali or - It's on the Railway station road (Serves both Rajasthani and Gujarathi thalis - They have a fixed menu which changes everyday.
A very romantic lakeside dining experience, do try either Ambrai or Upre (Both on banks of Pichola lake). While the former one can be accessed via your own vehicle, the second one will give you a local transport experience too, the open autos.
Go or order in from Jagdish Misthan Bhandar the crispiest pyaaz ki kachori with jalebi for breakfast - One outlet's at Chetak Circle and the other one at Surajpole. For the new age chaats (momos or gol gappe) - evening market at Sukadia Circle is a go-to place.
Looking for even more authentic Rajasthani food experience, visit Shilpgram - It's on the other side of lake Fatehsagar. If you are visiting in third or fourth week of December then you will be lucky to see the Annual festival it hosts where both performing artists and sellers come from around the country.
Last but not the least - Shopping.. Markets like Hathipole for artefacts and clothes, Ashok Nagar for high street brands and far distant Lakecity Mall in case you are missing your Metro city roots ;).. Also Shilpgram offers you a good Rajasthani culture to fill your bags and carry along..
Hope this serves as a good guide. Enjoy your stay and please be mindful of the cleanliness!